A071817 Number of 3-digit numbers whose digits add up to n.
1, 3, 6, 10, 15, 21, 28, 36, 45, 54, 61, 66, 69, 70, 69, 66, 61, 54, 45, 36, 28, 21, 15, 10, 6, 3, 1
Offset: 1
Examples
a(4) = 10 because there are 10 different 3-digit numbers whose digit sum is 4 (103, 112, 121, 130, 202, 211, 220, 301, 310, 400, which are the 3-digit elements of A052218).
Crossrefs
Cf. A071816.
Programs
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Maple
for i from 1 to 9*3 do a[i] := 0:od:for i from 100 to 999 dob := convert(i,base,10): s := sum(b[j],j=1..nops(b)):a[s] := a[s]+1:od:seq(a[j],j=1..3*9);
Formula
G.f.: (1 - x^10)^2*(x - x^10)/(1 - x)^3. - Miquel Cerda, Jul 09 2017
Extensions
Corrected and extended by Sascha Kurz, Feb 07 2003
Name clarified by Jon E. Schoenfield, Nov 20 2016
Comments